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How do you solve #3/(2x)-9/2=6x#?

Answer 1

Isaiah Anthony

#x=1/4, -1#

#3/(2x)-9/2=6x#

#3/(2x)-(9x)/(2x)=6x#

#(3-9x)/(2x)=6x#

#3-9x=12x^2#

#12x^2+9x-3 = 0#

#4x^2+3x-1=0#

#(4x-1)(x+1)=0#

#x=1/4, -1#

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Answer 2

Jace Anderson

To solve the equation 3/(2x) - 9/2 = 6x, we can follow these steps:

Multiply the entire equation by 2x to eliminate the denominators: 2x * (3/(2x)) - 2x * (9/2) = 2x * (6x)
Simplify the equation: 3 - 9x = 12x^2
Rearrange the equation to bring all terms to one side: 12x^2 + 9x - 3 = 0
Factor the quadratic equation or use the quadratic formula to solve for x.

Alternatively, if we cannot factor the equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 12, b = 9, and c = -3. Plugging these values into the quadratic formula will give us the solutions for x.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.